Effect of Thermal Bridges in Insulated Walls on Air-Conditioning Loads Using Whole Building Energy Analysis

sustainability

Article Effect of Thermal Bridges in Insulated Walls on Air-Conditioning Loads Using Whole Building Energy Analysis

Mohamed F. Zedan *, Sami Al-Sanea, Abdulaziz Al-Mujahid and Zeyad Al-Suhaibani

Mechanical Engineering Department, King Saud University, Riyadh 11421, Saudi Arabia; [email protected] (S.A.-S.); [email protected] (A.A.-M.); [email protected] (A.A.-S.) * Correspondence: [email protected]; Tel.: +966-50-895-4548

Academic Editor: Andrew Kusiak Received: 13 April 2016; Accepted: 9 June 2016; Published: 16 June 2016

Abstract: Thermal bridges in building walls are usually caused by mortar joints between insulated building blocks and by the presence of concrete columns and beams within the building envelope. These bridges create an easy path for heat transmission and therefore increase air-conditioning loads. In this study, the effects of mortar joints only on cooling and heating loads in a typical two-story villa in Riyadh are investigated using whole building energy analysis. All loads found in the villa, which broadly include ventilation, transmission, solar and internal loads, are considered with schedules based on local lifestyles. The thermal bridging effect of mortar joints is simulated by reducing wall thermal resistance by a percentage that depends on the bridges to wall area ratio (TB area ratio or Amj/Atot) and the nominal thermal insulation thickness (Lins). These percentage reductions are obtained from a correlation developed by using a rigorous 2D dynamic model of heat transmission through walls with mortar joints. The reduction in thermal resistance is achieved through minor reductions in insulation thickness, thereby keeping the thermal mass of the wall essentially unchanged. Results indicate that yearly and monthly cooling loads increase almost linearly with the thermal bridge to wall area ratio. The increase in the villa’s yearly loads varies from about 3% for Amj/Atot = 0.02 to about 11% for Amj/Atot = 0.08. The monthly increase is not uniform over the year and reaches a maximum in August, where it ranges from 5% for Amj/Atot = 0.02 to 15% for Amj/Atot = 0.08. In winter, results show that yearly heating loads are generally very small compared to cooling loads and that heating is only needed in December, January and February, starting from late night to late morning. Monthly heating loads increase with the thermal bridge area ratio; however, the variation is not as linear as observed in cooling loads. The present results highlight the importance of reducing or eliminating thermal bridging effects resulting from mortar joints in walls by maintaining the continuity of the insulation layer in order to reduce energy consumption in air-conditioned buildings.

Keywords: thermal bridges; mortar joints; transmission load; R-value; wall thermal performance; building envelope

1. Introduction Thermal bridges in the outer walls of buildings are typically caused by mortar joints between insulated building blocks and by concrete structural elements, such as columns, beams and slabs. These bridges create an easy path for heat transfer across the building envelope and usually result in increased heating and cooling loads in buildings. Accurate thermal bridging assessment is becoming extremely important not only in predicting peak thermal loads and yearly heating/cooling loads, but also in estimating the potential for condensation and subsequent mold growth in the heating season in

Sustainability 2016, 8, 560; doi:10.3390/su8060560 www.mdpi.com/journal/sustainability Sustainability 2016, 8, 560 2 of 20 cold climates. The main difficulty in modeling thermal bridges stems from the fact that they create significantSustainability two-dimensional 2016, 8, 560 (2D) effects on heat transmission across building walls in the2 of case 21 of mortar joints and three-dimensional (3D) effects in the case of concrete structural elements. At the samesignificant time, most two-dimensional building energy (2D) simulation effects on computer heat transmission packages across utilize building one-dimensional walls in the case models of in ordermortar to simplify joints lengthyand three-dimensional calculations. (3D) effects in the case of concrete structural elements. At the same time, most building energy simulation computer packages utilize one-dimensional models in The literature survey reported in the next section shows that most studies on thermal bridges order to simplify lengthy calculations. consider mainlyThe literature those caused survey byreported structural in the elements next sect andion shows that little that attention most studies was on given thermal to mortar bridges joints. To remedyconsider this mainly deficiency, those thecaused present by structural investigation elemen dealsts and with that the little effects attention of mortar was given joints to in mortar the walls of a typicaljoints. To villa. remedy When this using deficiency, insulated the present building investigation blocks, mortar deals with joints thecause effectsdiscontinuities of mortar joints in the insulationthe walls layer(s) of a typical along villa. the wall When height, using asinsulated shown building in Figure blocks,1, and mortar therefore joints provide cause discontinuities little resistance to heatin transmissionthe insulation comparedlayer(s) along to thethe insulationwall height, layer as shown itself. in This Figure affects 1, and adversely therefore theprovide effectiveness little of thermalresistance insulation, to heat resultingtransmission in considerablecompared to the reduction insulation in layer theR-value itself. This of theaffects wall adversely compared the to a wall witheffectiveness a continuous of thermal insulation insulation, layer. resulting Using in a 2Dconsiderable dynamic reduction model for in heat the R-value transmission of the throughwall compared to a wall with a continuous insulation layer. Using a 2D dynamic model for heat a typical wall section with mortar joints, Al-Sanea and Zedan [1] showed that the reduction in the transmission through a typical wall section with mortar joints, Al-Sanea and Zedan [1] showed that R-value depends on both the ratio of the thermal bridge area to wall area (TB ratio or A /A ) and the reduction in the R-value depends on both the ratio of the thermal bridge area to wall mjarea (TBtot the insulation thickness (L ). In the present paper, we deal with a whole building (villa) rather than a ratio or Amj/Atot) and insthe insulation thickness (Lins). In the present paper, we deal with a whole wall sectionbuilding [1 (villa)] to study rather the than effects a wall of section thermal [1] bridges to study on the the effects hourly, of thermal monthly bridges and yearly on the coolinghourly, and heatingmonthly loads, and under yearly Riyadh cooling ambient and heating conditions. loads, Allunde loadsr Riyadh found ambient in a typical conditions. villa All are loads considered found in using wholea buildingtypical villa energy are considered analysis. Theseusing whole loads broadlybuilding includeenergy analysis. ventilation These loads, loads solar broadly loads, include internal loadsventilation (lights, people, loads, equipment,solar loads, internaletc., with loads typical (lights, schedules people, equipment, based on localetc., with lifestyles) typical andschedules of course heat transmissionbased on local through lifestyles) the and villa’s of course envelope, heat transm withission the latter through being the thevilla’s dominant envelope, load with under the latter Riyadh ambientbeing conditions. the dominant load under Riyadh ambient conditions.

Hmj Mortar joint

Masonry

Hb Insulation

Masonry with air space

Outside Inside

FigureFigure 1. Diagrammatic 1. Diagrammatic sketch sketch showing showingthermal thermal bridges ca causedused by by mortar mortar joints joints in building in building walls. walls.

The thermal bridging effect resulting from mortar joints is simulated, in the present work, by Thereducing thermal the wall bridging thermal effect resistance resulting (R-value) from by mortar a percentage joints that is simulated, corresponds in to the the presentbridge to work, wall by reducingarea theratio wall and thermal the nominal resistance thickness (R-value) of the insulati by a percentageon layer. The that percentage corresponds reduction to thein the bridge R-value to wall area ratiois obtained and the from nominal a graphical thickness correlation of the developed insulation from layer. detailed The percentage and rigoro reductionus 2D dynamic in the analysis R-value is obtainedof heat from transmission a graphical through correlation the same developed wall section from that detailed includes and mortar rigorous joints, 2D in dynamica way similar analysis to of heat transmissionthe study presented through by thethe sameauthors wall in sectionAl-Sanea that and includes Zedan [1]. mortar The reduction joints, in in a waywall R-value similar tois the studyachieved presented by by reducing the authors the insulation in Al-Sanea thickness and Zedan and thereby [1]. The keeping reduction the thermal in wall mass R-value of the is achievedwall by reducingessentially the unchanged. insulation thicknessThe whole and building thereby lo keepingad simulation the thermal package mass used of thein wallthe present essentially

Sustainability 2016, 8, 560 3 of 20 unchanged. The whole building load simulation package used in the present investigation is the Hourly Analysis Program provided to the authors by the Carrier Corporation. This package, which is known as HAP [2], is based on ASHRAE load calculation procedures and is therefore extensively used by designers of air-conditioning systems and energy engineers worldwide for load estimation and building energy simulation. This package and two other commercial packages were validated in a doctoral dissertation [3] for an actual building at Iowa State University by comparison with measurements. Al-Tahat and Al-Ali [4] validated the HAP energy simulation feature by comparing the historical energy consumption data and simulation results of an existing building before applying any energy saving measures. The deviation between HAP results and actual data was within 5%. The research background of thermal bridges is reviewed next, followed by a short description of the present case study. A summary of the 2D dynamic heat transfer model used to account for the effect of mortar joints on wall thermal resistance and to develop the correlation for these effects is given next. The results of the whole building energy analysis of the simulated effects of thermal bridges are then presented.

2. Research Background Asdrubali et al. [5] proposed a quick and approximate methodology to perform quantitative analysis of thermal bridges, through thermographic surveys of the wall surface followed by analytical processing. From the simple measurement of the air temperature and the analysis of the thermograph, the thermal bridge effect can be estimated as a percentage increase over the same wall, but with homogenous transmittance. Ascione et al.[6] compared different methods for modelling thermal bridges created by flat heterogeneous concrete slabs in a multistory office building, as well as the results of energy simulation programs for Italian climates. The methods used are simplified 1D models with a homogeneous structure and more sophisticated 2D or 3D models. They concluded that proper modelling of thermal bridges is necessary. Hassid [7] presented an integral approach to calculate thermal bridge effects at the junction between dissimilar, multilayer walls. The model is based on the solution of the integrated 2D conduction equation for the main wall and the thermal bridge. The predicted overall heat transfer coefficients and minimum internal surface temperatures are shown to compare favorably with proper computational solution. However, this 2D model is limited to a steady state solution that ignores both solar radiation and long wave radiation at the outside surface. Martin et al.[8] investigated the problems encountered in the calculation of thermal bridges under dynamic conditions considering their thermal inertia when using energy simulation programs. They pointed out the need for proper treatment as the TB effect becomes more pronounced at the high insulation thicknesses required by building codes in recent years. The study was carried out for thermal bridges with thermal inertia similar to the homogenous wall and for thermal bridges with much lower inertia. Martin with others [9] followed up on this study by carrying out a series of experiments in a guarded hot box testing facility to study the thermal response of pillar-type thermal bridges under both steady and dynamic conditions. One of the main objectives of this study was the determination of the influence of the area of the thermal bridge on heat transfer across building walls. The test results were compared to those obtained from building energy simulation. The authors pointed out that there is a great deal of uncertainty regarding the dynamic behavior of thermal bridges when using energy simulation programs. They concluded that proper treatment of thermal bridges and their in situ construction is necessary for calculating the overall thermal demand of buildings. Evola et al.[10] presented a study on the effects of thermal bridges for two building types, terraced houses and semi-detached houses, considering three envelope designs commonly used in Italy for the mild Mediterranean climate. The buildings are characterized by a reinforced concrete structure and clay block walls. The thermal performance of the envelopes complies with Italian regulations for new construction. The impact of thermal bridges on both heating and cooling loads was studied first. Then, the economic value of correcting such thermal bridges, while considering additional costs of construction and refurbishment, was assessed by calculating the discounted payback period. Sustainability 2016, 8, 560 4 of 20

One of the methods the author considered to correct or reduce the effects of thermal bridges is to cover the whole wall by insulated boards. Unfortunately, the cost-benefit analysis has shown that the savings produced by rectifying thermal bridge effects are not sufficient to recover the additional costs of construction and refurbishment. However, one should realize that such a conclusion is valid for the methods that the authors used to reduce the effects of thermal bridges under mild Mediterranean climatic conditions and, therefore, should not be generalized. Gao et al. [11] used state model reduction techniques to develop a low-order (reduced) three-dimensional heat transfer model by including terms for the additional losses/gains through thermal bridges in their analysis. The authors validated this model in both frequency and time domains. The model was then implemented in the software package “TRNSYS” resulting in a large reduction in the amount of calculations in time simulations. Ben-Nakhi [12] presented a dynamic thermal bridging assessment module that is integrated within a whole building simulation environment with more realistic boundary conditions. It integrates all inter-related energy subsystems that exist in buildings. More recent studies by Bianchi et al.[13] and Cuce and Cuce [14] focused on experimental investigation to analyze thermal bridging effects. Bianchi et al. [13] carried out in-field experimental measurements in order to evaluate energy losses through the envelope of a test room. Infrared thermography and the so-called “incidence factor of thermal bridges”, proposed in a previous study by the same authors, were applied to assess the energy losses due to thermal bridges. The incidence factor of thermal bridges was based on indoor air temperature, surface temperature and thermal fluxes throughout the building envelope. This factor represented the ratio between thermal transmittance in the presence of a thermal bridge to that in its absence and could be considered as a thermal bridge correction factor. Results showed that the overall effect of thermal bridges in increasing thermal losses through the building envelope corresponded to about 9%. It is interesting to note that the current study adopts a similar approach in presenting the effects of thermal bridges, but with using whole building energy analysis. Cuce and Cuce [14] presented an experimental and statistical study for evaluating thermal bridges at internally retrofitted walls of a test room. It was concluded that the mere internal retrofit was not a decisive solution to reduce the heat loss from residential buildings if additional proper attention was not paid to non-insulated building elements. Although expensive, vacuum insulation panels (VIPs) are characterized by very low thermal conductivity, compared to traditional insulating materials, and hence, can improve the thermal behavior of buildings, especially in the case of energy retrofitting [15]. However, VIPs require the manufacturing of prefabricated panels of a fixed shape/size, which means that their use in the building envelope involves the problem of joining the panels to each other and of fixing them onto additional supporting structures. The problem with this technique is that these structures and systems themselves cause thermal bridging effects. The energy performance of the resulting insulation package can therefore be affected to a great extent by these additional elements and can become significantly lower than that of the VIP panel alone. Using a heat flux meter, Lorenzati et al.[15] carried out experiments in order to verify the effect of thermal bridges on the energy performance of VIPs. Results were used to calibrate and verify a numerical model that allowed the performance of various VIP joint materials/typologies to be predicted and the performance of the overall package to be optimized. Quinten and Feldheim [16] reviewed and tested different approaches for modeling the heat transfer through a thermal bridge with implementation into building energy simulation programs. The approaches were based on an equivalent wall method. The equivalent wall replaces the thermal bridge by having the same steady and dynamic thermal behavior as the thermal bridge. The authors proposed a new method, which was a mix between the principles of the structure factors method and a harmonic method. The mixed method was tested on a 2D thermal bridge, the junction between the floor and exterior wall, and was found to lead to accurate results and a unique solution. Martins et al.[17] assessed several thermal bridge mitigation strategies to improve the thermal performance of a lightweight steel-framed (LSF) wall module and to reduce energy consumption. The implementation of thermal bridges’ mitigation strategies in a modular LSF wall was performed using 3D FEM models. Sustainability 2016, 8, 560 5 of 20

The implementation of those mitigation strategies led to a reduction of 8.3% in the U-value. An optimization of the wall module insulation layers was also performed, which, combined with the mitigation approaches, allowed a decrease of 68% in the U-value. Design rules for lightweight steel-framed elements were also presented. Two international standards (EN ISO 10211 [18] and EN ISO 14683 [19]) are frequently referred to by researchers in this area. ISO 2011 [18] lays out the specifications for the 3D and 2D geometrical models of a thermal bridge for the numerical calculation of heat flows, in order to assess the overall heat loss from a building or part of it and the minimum surface temperatures, in order to assess the risk of surface condensation, assuming all physical properties are independent of temperature and no heat sources within the building element. International Standard ISO 14683 [19] deals with simplified methods for determining heat flows through linear thermal bridges that occur at junctions of building elements. Furthermore, it specifies manual calculation methods related to thermal bridges. Unfortunately, the thermal bridges covered in these two standards are those caused by structural elements and not by mortar joints. In summary, as was mentioned in the Introduction, the research background showed that most previous studies on thermal bridging effects focused on bridges caused by structural elements and that little attention was given to mortar joints. The present study quantifies the effects of mortar joints in building walls on whole building energy consumption through modifying the conductive wall thermal resistance. It is noted that the thermal inertia per unit mass of the mortar joints is effectively the same as the bulk masonry.

3. Description of the Case Study

3.1. General The building under consideration is a two-story villa (detached home) located in Riyadh. The total floor area is 400 m2 (200 m2 each level). The building plans for the villa are shown in Figure2. The ground floor of the villa consists of a formal reception area, formal dining room, family room, toilets and kitchen. The first floor consists of four bedrooms, a living space/games area and bathrooms. The remaining overall building characteristics are: average ceiling height = 2.8 m above the floor, roof height of about 5.6 m above the grade level, 16 windows (two on each of the north, south, west and east sides per floor) and two doors, one on the east side and another on the south side. A full description of the wall construction, roof construction and window construction, as well as their thermal properties is given in the next few sections. This is followed by energy simulation data.

3.2. Wall and Roof Construction Figure3 shows the construction of villa walls, which are basically built of insulated building blocks commonly used in Saudi Arabia and covered by two layers of plaster. The thickness of the insulation layer in the block Lins is 75 mm and made of molded polystyrene. Please note that the ﬁgure shows a cyclic part of the wall section that is repeated along the wall height. A photograph of the type of block modeled is shown in AppendixA. The roof construction is shown in Figure4. Note that the insulation material for the roof is high-density molded polystyrene with a thickness Lins = 48 mm. The properties of the wall and roof materials are shown in Table1 below. The properties of the masonry materials are obtained mostly from the ASHRAE Handbook of Fundamentals [20]. The properties of the insulating materials vary according to the type of material and depend on many other factors, such as density, moisture content, temperature, aging, storage conditions, etc. The properties of molded polystyrene given in Table1 for the walls and roof are speciﬁc to materials produced by local Saudi manufacturers as measured at room temperature by Al-Kasmoul [21]. It is interesting to note that the densities of insulation materials used in roofs are commonly higher than the densities of the same type of insulation materials used in walls in order to withstand higher pressure. Accordingly, the thermal Sustainability 2016, 8, 560 6 of 20 conductivities (as well as the costs) are different between the same type of insulation materials used in roofsSustainability and walls. 2016, 8, 560 6 of 21

(a)

(b) Figure 2. Building plans of the villa case study. (a) Ground floor plan; (b) first floor plan. Figure 2. Building plans of the villa case study. (a) Ground floor plan; (b) first floor plan.

SustainabilitySustainability 20162016,, 88,, 560560 77 ofof 2121

3.2.3.2. WallWall andand RoofRoof ConstructionConstruction FigureFigure 33 showsshows thethe constructionconstruction ofof villavilla walls,walls, whichwhich areare basicallybasically builtbuilt ofof insulatedinsulated buildingbuilding blocksblocks commonlycommonly usedused inin SaudiSaudi ArabiaArabia andand coveredcovered byby twotwo layerslayers ofof plaster.plaster. TheThe thicknessthickness ofof thethe insulation layer in the block Lins is 75 mm and made of molded polystyrene. Please note that the insulation layer in the block Lins is 75 mm and made of molded polystyrene. Please note that the figurefigure showsshows aa cycliccyclic partpart ofof thethe wallwall sectionsection thatthat isis repeatedrepeated alongalong thethe wallwall height.height. AA photographphotograph ofof thethe typetype ofof blockblock modeledmodeled isis shownshown inin AppendixAppendix A.A. ThThee roofroof constructionconstruction isis shownshown inin FigureFigure 4.4. NoteNote that the insulation material for the roof is high-density molded polystyrene with a thickness Lins = 48 that the insulation material for the roof is high-density molded polystyrene with a thickness Lins = 48 mm.mm. TheThe propertiesproperties ofof thethe wallwall andand roofroof materialsmaterials areare shownshown inin TableTable 11 below.below. TheThe propertiesproperties ofof thethe masonrymasonry materialsmaterials areare obtainedobtained mostlymostly fromfrom ththee ASHRAEASHRAE HandbookHandbook ofof FundamentalsFundamentals [20].[20]. TheThe propertiesproperties ofof thethe insulatinginsulating materialsmaterials varyvary accordaccordinging toto thethe typetype ofof materialmaterial andand dependdepend onon manymany otherother factors,factors, suchsuch asas density,density, moisturemoisture contcontent,ent, temperature,temperature, aging,aging, storagestorage conditions,conditions, etcetc.. TheThe propertiesproperties ofof moldedmolded polystyrenepolystyrene givengiven inin TableTable 11 forfor thethe wallswalls andand roofroof areare specificspecific toto materialsmaterials producedproduced byby locallocal SaudiSaudi manufacturersmanufacturers asas measuredmeasured atat roomroom temperaturetemperature byby Al-KasmoulAl-Kasmoul [21].[21]. ItIt isis interestinginteresting toto notenote thatthat thethe densitiesdensities ofof insulatiinsulationon materialsmaterials usedused inin roofsroofs areare commonlycommonly higherhigher thanthan thethe densitiesdensities ofof thethe samesame typetype ofof insulationinsulation materialsmaterials usedused inin wallswalls inin orderorder toto withstandwithstand higherhigher pressure.pressure.Sustainability Accordingly,Accordingly,2016, 8, 560 thethe thermalthermal conductivitiesconductivities (as(as wellwell asas thethe costs)costs) areare differentdifferent betweenbetween7 ofthethe 20 samesame typetype ofof insulationinsulation materialsmaterials usedused inin roofsroofs andand walls.walls.

FigureFigure 3.3. CyclicCyclicCyclic part partpart (symmetric (symmetric(symmetric region) region)region) of wallofof wallwall structure ststructureructure showing showingshowing a ﬁve-layer aa five-layerfive-layer building buildingbuilding block covered blockblock coveredcoveredby two cement byby twotwo plastercementcement layers plasterplaster and layelaye ars mortarrs andand aajoint mortarmortar cutting jointjoint across cuttingcutting the acroacro block;ssss thethe dimensions block;block; dimensionsdimensions in mm. inin mm.mm.

Figure 4. Schematic of a vertical roof section showing various layers (Dimensions. in mm, NTS). FigureFigure 4.4. SchematicSchematic ofof aa verticalvertical roofroof sectionsection showinshowingg variousvarious layerslayers (Dimensions.(Dimensions. inin mm,mm, NTS).NTS).

Table 1. Wall and roof material properties [20,21].

Material k (W/m¨ K) ρ (kg/m3) c (J/kg¨ K) Cement plaster 0.72 1860 840 Concrete 1.73 2243 840 Molded polystyrene (wall) 0.034 23 1280 Air space keff = 0.167 1.1 1007 Molded polystyrene (roof) 0.033 38 1280 Tiles 0.84 1900 840 Mortar bed 0.72 1860 840 Membrane 0.5 1700 1000 Foam concrete 0.2 640 840 Reinforced concrete 2.3 2411 800 Heavyweight concrete 1.73 2243 840

3.3. Window Data All windows are identical with the following data: Sustainability 2016, 8, 560 8 of 20

Dimensions: W = 0.91 m (3 ft) ˆ H= 1.52 m (5 ft) Frame type: aluminum with thermal breaks Internal shading: drapes, open weave, medium Overall shading coefficient = 0.54 Overall U-value= 3.1 W/m2¨ K Glazing: double pane with a 6-mm air-space: Outer glazing: a 3-mm gray tint with 0.631 transmissivity, 0.06 reflectivity and 0.304 absorptivity Inner glazing: 3 mm, clear, with 0.841 transmissivity, 0.078 reflectivity and 0.081 absorptivity

3.4. Other Energy Simulation Data With regard to weather conditions, HAP provides simulation weather data covering one full year for a large number of cities around the world, including Riyadh, as a built-in feature. These weather data are obtained from the IWEC (International Weather Year for Energy Calculation) data files released by ASHRAE in 2000 [22]. These datasets contain “typical” weather data intended for use with building energy simulation programs. The IWEC datasets utilize 18 years of hourly data by the National Climatic Data Center for 227 locations outside the USA and Canada. The international climatic zone number for Riyadh is one. The cooling degree days (CDD) are about 3500 ˝C and the heating degree days (HDD) are 410 ˝C for 18 ˝C base temperature. Figure5 shows the temperature and solar-radiation profiles during the month of August, as an example. The villa building is supported by a concrete slab that sits on the ground (slab on grade). The area of the slab is 200 m2, and its perimeter is 56.7 m. The exchange of heat between the indoor air within the ground floor and the soil occurs through the slab. This has been taken into consideration in the software. The U-coefficient for the slab is 0.568 m2¨ K/W. The indoor temperature set points are: 23 ˝C for cooling and 22 ˝C for heating. The input data for internal heat gains are specified for each internal source (people, lighting, equipment, such as TVs, cooking appliances, computers, etc.) with its own specific schedule. These data are summarized as follows: six people (sedentary) in the villa; 2000 W lighting, 600 W equipment and 4000 W kitchen on the ground floor, in addition to 800 W lighting and 300 W TV on the first floor. The input data for ventilation, with regard to the outdoor air requirements, are taken according to the ASHRAE STD 62.1–2007 [23], using values for residential dwelling unit. These values are 2.5 L/s per person and 0.3 L/s per square meter of floor area. This results in a 150-L/s ventilation rate, which was fixed throughout the year to ensure good indoor air quality via the constant volume AC system described later. For building weight input data, HAP offers options for light, medium and heavy construction. Although it is possible to specify values in between, we selected heavy construction since this is the closest to our case. Regarding the selected HVAC system, there are a number of equipment options available for the air-conditioning of a typical villa in Riyadh. The system chosen for the villa under consideration is a roof-top packaged unit for cooling with an air-source heat pump for heating. In such a unit, all HVAC equipment is in one package from which conditioned air is fed to various spaces in the villa via a simple duct system ending with simple diffuser(s) in each space. Such a system is fairly common in above-average and upscale villas in Riyadh. The air distribution system is a constant volume system. Cooling capacity is controlled by cycling the compressor on and off, via a thermostat, while the fan is kept on as long as the system is on. Since our concern is the effect of thermal bridges in a typical Saudi home and not the air conditioning (AC) system design, the villa is treated as one single AC zone, which by the way, is the case in most existing villas with constant volume systems. Of course, one will have better control of temperature with a multi-zone system; however, constant volume multi-zone systems are energy inefficient because of using reheating to control temperature in various zones. Sustainability 2016, 8, 560 9 of 21 heavySustainability construction.2016, 8, 560 Although it is possible to specify values in between, we selected heavy9 of 20 construction since this is the closest to our case.

Dry Bulb Wet Bulb 50

) 35 癈

Temperature ( Temperature 20 Temperature (°C) 15

213 215 217 219 221 223 225 227 229 231 233 235 237 239 241 243 214 216 218 220 222 224 226 228 230 232 234 236 238 240 242 Day of Year (a)

Beam Solar on Horiz. Total Solar on Horiz. 1000

900 800

) 700 2 600 500

400

Solar Flux ( W/m?) 300 Solar Flux (W/m 200

100

0 213 215 217 219 221 223 225 227 229 231 233 235 237 239 241 243 214 216 218 220 222 224 226 228 230 232 234 236 238 240 242 Day of Year (b)

Figure 5. Riyadh sample weather data used in the simulation: 1 August (Day 213) through 31 August Figure 5. Riyadh sample weather data used in the simulation: 1 August (Day 213) through 31 (Day 243). (a) Dry-bulb and wet-bulb temperature profiles; (b) Profiles of Solar flux on a horizontal August (Day 243). (a) Dry-bulb and wet-bulb temperature profiles; (b) Profiles of Solar flux on a plane. horizontal plane.

Regarding the selected HVAC system, there are a number of equipment options available for 4. Simulation of Effects of Thermal Bridges Using a 2D Dynamic Heat Transfer Model the air-conditioning of a typical villa in Riyadh. The system chosen for the villa under consideration is a roof-topThe effect packaged of the thermal unit for bridges cooling is with simulated an air-source in the whole heat pump building for analysis heating. by In reducing such a unit, the wallall HVACthermal equipment resistance is by in a percentageone package that from depends which on conditioned the thermal air bridge is fed to to wall various area ratiospaces (A mjin/A thetot villa) and viaon a the simple nominal duct thickness system ofending thermal with insulation simple (Ldiffins).user(s) These in % reductionseach space. are Such obtained a system from is studying fairly commonthe heat transferin above-average across the and wall upscale with and villas without in Riyadh. thermal The bridges air distribution under 2D dynamic system steady is a constant periodic volumeconditions system. using Cooling a model capacity developed is previouslycontrolled byby thecycling ﬁrst twothe authors.compressor This on model and is off, detailed via a in thermostat,Al-Sanea and while Zedan the [fan1] and is kept is summarized, on as long foras th completeness,e system is on. in theSince next our section. concern is the effect of thermal bridges in a typical Saudi home and not the air conditioning (AC) system design, the villa is treated4.1. Two-Dimensional as one single AC Dynamic zone, Model which for by a Wallthe way, with Thermalis the case Bridges in most existing villas with constant volumeIn systems. this section, Of course, we present one onlywill thehave main better features control of of the temperature model. Figure with1 shows a multi-zone the overall system; wall section where mortar joints cut across the insulation layer causing the thermal bridge, while Figure3

Sustainability 2016, 8, 560 10 of 20 shows a symmetric (cyclic) region of the wall section with all details. This symmetric region, which is repeated along the wall height, has a bottom symmetry plane passing through the middle of the building block and a top symmetry plane passing through the middle of the mortar joint. The outside surface of the wall is exposed to convection heat transfer (qc,o), long wave radiation exchange with surroundings (qr,o) and solar radiation (Is). The inside surface is exposed to combined convection and radiation (qi) heat transfer, which represent the rate of heat transmission into the inner space (transmission load). For no heat generation, constant properties, 2D and negligible interface resistance, the equation governing time-dependent heat ﬂow in the composite structure shown in Figure3 is reduced to the Poisson equation, namely: B BTj B BTj BTj k ` k “ pρcq (1) Bx j Bx By j By j Bt ˆ ˙ ˆ ˙ where the subscript j refers to wall layers (i.e., j = 1, 2, ... , N). The sought after solution of Equation (1) is T(x,y,t), where x is the coordinate normal to wall layers and y is the coordinate along the wall height, as shown in Figure3. The solution T(x,y,t) requires an initial condition and boundary conditions at all boundaries. All layers are assumed to be initially at the mean ambient temperature, T0.

Tj(x,y,0) “ T0 (2)

The steady periodic solution is independent of T0. The boundary conditions are as follows:

BT ´ k “ h T ´ T (3) N Bx i x“L f,i ˇx“L ˇ ` ˘ ˇ at the inside surface where layer N lies on theˇ inside, kN is the thermal conductivity of layer N, hi is the inside surface combined convection and radiation heat transfer coefﬁcient, Tf,i is the indoor air temperature, and: BT ´k “ h T ´ T ` λI ` q (4) 1 Bx c,o f,o x“0 s r,o ˇx“0 ˇ ` ˘ at the outside surface, where Layerˇ 1 lies on the outside, k is the thermal conductivity of Layer ˇ 1 1, hc,o is the outside surface convection coefﬁcient, Tf,o is the outdoor air temperature and λ is the solar absorptivity. At the planes of symmetry (y = 0 and y = H), the temperature gradient normal to either plane is zero, i.e., BT BT “ “ 0 (5) By By ˇy“0 ˇy“H ˇ ˇ ˇ ˇ Equation (1) is solved numerically byˇ a computer.ˇ Details of the numerical model and the computer solution of the above equations are given in Al-Sanea and Zedan [1].

∂T ∂T = = 0 ∂ ∂ (5) y y=0 y y=H

Equation (1) is solved numerically by a computer. Details of the numerical model and the computer solution of the above equations are given in Al-Sanea and Zedan [1].

4.2. Results of the 2D Dynamic Thermal Bridge Model The above model was run for the wall shown in Figure 3 with different TB area ratios for a single nominal insulation thickness in a previous investigation [1]. In the present study, this work is extended to cover various nominal insulation thicknesses in order to obtain a more generalized correlation for the effect of thermal bridges under 2D dynamic conditions. Such a correlation would be useful for use in the future for wall structures similar to the present wall, but with different insulation thicknesses. The results for the transmission load are obtained from the numerical solution on an hourly basis over a full year. The hourly results are integrated to obtain the transmission load on a monthly Sustainability 2016, 8, 560 11 of 20 and yearly basis. The percentage increase in the yearly transmission load over the corresponding load without thermal bridges is shown in Figure 6a versus the TB percentage area ratio % Amj for different nominal insulation thicknesses Lins. Please note that % Amj is basically 100 × Amj/Atot, where Amj/Atot = mortar joint height Hmj divided by the block height Hb. The results in the figure show that Amj/Atot = mortar joint height Hmj divided by the block height Hb. The results in the figure show that the % increase in transmission load increases with the TB area ratio as expected for a given Lins and the % increase in transmission load increases with the TB area ratio as expected for a given Lins and increases with L for a given TB area ratio. This confirms observations by previous investigators that increases withins Lins for a given TB area ratio. This confirms observations by previous investigators higherthat insulation higher insulation thicknesses thicknesses accentuate accent the effectsuate the of effects thermal of bridgesthermal [ 8bridges]. The increase[8]. The inincrease transmission in load astransmission a result of load thermal as a result bridges of thermal is equivalent bridges is to equivalent a drop in to the a drop dynamic in the dynamic R-value R-value of the wall.of the The correspondingwall. The corresponding correlation for correlation the reduction for the reduction in R-values in R-values is shown is shown in Figure in Figure6b. The 6b. resultsThe results in that figurein indicate that figure that indicate the drop that in the R-values drop in increasesR-values increases with the with TB areathe TB ratio area for ratio a givenfor a given value value of L insof and Lins and increases with Lins for a given TB area ratio and that such a drop can reach more than 50%. increases with Lins for a given TB area ratio and that such a drop can reach more than 50%.

Sustainability 2016, 8, 560 12 of 21 (a)

(b)

FigureFigure 6. 6.Two-dimensional Two-dimensional study results results for for the the effect effect of % of thermal % thermal bridge bridge (TB) area (TB) ratio area for ratio various for variousnominal nominalinsulation insulation thicknesses: thicknesses: (a) percentage (a) percentage increase in increase yearly heat in yearly transmission heat transmission load; (b) percentage load; (b decrease) percentage in decreaseyearly-averaged in yearly-averaged dynamic thermal dynamic resistance. thermal resistance.

4.3. Utilization of the 2D Dynamic Thermal Bridge Model Results in Whole Building Simulation The thermal bridging effect resulting from mortar joints is simulated, in the present whole building analysis, by reducing the wall thermal resistance (R-value) by a percentage that corresponds to the bridge to wall area ratio and the nominal thickness of the insulation layer. The percentage reduction in the R-value is obtained from the graphical correlation developed from the 2D dynamic analysis described above and presented in Figure 6b. In the whole building energy analysis of the villa reported in the next section, the values for the percentage reduction in the wall R-values are picked up from the curve representing the 75-mm insulation thickness (in Figure 6b), which is the value of Lins in the villa’s walls. One of the most convenient ways to simulate the reduction in the R-value of the wall in whole building analysis is by reducing the thickness of the insulation layer. This is the route selected in the present study in order not to alter the wall thermal mass and therefore not to affect the dynamic characteristics of the original wall. The simulation program is run with the input data described in Section 3 previously and with walls having a 75-mm insulation thickness in order to establish the baseline case of no thermal bridges (Amj/Atot = 0) for this investigation. The simulation is then run multiple times, each time representing a different TB area ratio (Amj/Atot). Different TB area ratios are represented in the simulation via adjusting the insulation thickness to a value that corresponds to the Amj/Atot ratio for which the run is made, as shown in Table 2.

Table 2. Adjusted insulation thicknesses for simulating thermal bridge effects.

% Reduction in R-value Radjusted Lins, adjusted Amj/Atot (from 2D Correlation in Figure 6b) (m2·K/W) (mm) 0 (Baseline case) 0 2.660 75.00 0.02 22.5 2.062 54.65 0.04 35.0 1.729 43.35 0.06 42.9 1.519 36.20

Sustainability 2016, 8, 560 12 of 20

4.3. Utilization of the 2D Dynamic Thermal Bridge Model Results in Whole Building Simulation The thermal bridging effect resulting from mortar joints is simulated, in the present whole building analysis, by reducing the wall thermal resistance (R-value) by a percentage that corresponds to the bridge to wall area ratio and the nominal thickness of the insulation layer. The percentage reduction in the R-value is obtained from the graphical correlation developed from the 2D dynamic analysis described above and presented in Figure6b. In the whole building energy analysis of the villa reported in the next section, the values for the percentage reduction in the wall R-values are picked up from the curve representing the 75-mm insulation thickness (in Figure6b), which is the value of L ins in the villa’s walls. One of the most convenient ways to simulate the reduction in the R-value of the wall in whole building analysis is by reducing the thickness of the insulation layer. This is the route selected in the present study in order not to alter the wall thermal mass and therefore not to affect the dynamic characteristics of the original wall. The simulation program is run with the input data described in Section3 previously and with walls having a 75-mm insulation thickness in order to establish the baseline case of no thermal bridges (Amj/Atot = 0) for this investigation. The simulation is then run multiple times, each time representing a different TB area ratio (Amj/Atot). Different TB area ratios are represented in the simulation via adjusting the insulation thickness to a value that corresponds to the Amj/Atot ratio for which the run is made, as shown in Table2.

Table 2. Adjusted insulation thicknesses for simulating thermal bridge effects.

% Reduction in R-value 2 Amj/Atot (from 2D Correlation Radjusted (m ¨ K/W) Lins, adjusted (mm) in Figure6b) 0 (Baseline case) 0 2.660 75.00 0.02 22.5 2.062 54.65 0.04 35.0 1.729 43.35 0.06 42.9 1.519 36.20 0.08 48.5 1.370 31.14

It is interesting to note here that the effective R-value of the wall drops from 2.66 to 1.37 m2¨ K/W as a result of mortar joints with an area ratio of 8%. Because of the small density of polystyrene compared to other wall layers, the changes in wall thermal mass are negligibly small for the insulation thickness adjustments reported in Table2. The value of the thermal resistance for walls as recommended by the Saudi Building Code (SBC-Section 601, Energy Conservation), is obtained from a chart provided in the code at the degree days of Riyadh (CDD = 3500). The U-coefﬁcient obtained from the chart is 0.7 W/m2¨ K, which corresponds to an R-Value of 1.43 m2¨ K/W. The R-values in the above table exceed this value, except for the case with a TB ratio of 0.08.

4.4. Representative Results of the Whole Building Energy Simulation Before running the energy simulation, we have to make a design run to obtain the design load for each value of the thermal bridge ratio. Design cooling loads are summarized in Table3 below. The maximum value for the cooling load per unit area is 53.1 W/m2, or 18.8 m2/kW (66 m2/TR). We could not find any Saudi standards that stipulate target loads per unit area and classify residential building efficiency accordingly. However the above values indicate a highly efficient building when compared with some rules of thumb used by some engineers for rough estimate of loads based on area. After design runs were made, the simulation feature of HAP was run on an hourly basis for one full year. Sample results are presented next; for more details and for the villa’s daily and hourly cooling and heating loads, the reader may refer to Al-Sanea et al. [24]. Sustainability 2016, 8, 560 13 of 20

Table 3. Design cooling loads of the villa building as obtained from HAP.

Design Cooling Load (kW) Design Cooling Load per Unit Floor Area (W/m2) A /A mj tot Coil Space Coil Space 0 (Baseline case) 19.3 13.9 48.3 34.8 0.02 20.0 14.4 50 36 0.04 20.4 14.9 51 37.2 0.06 20.9 15.3 52.1 38.2 0.08 21.3 15.6 53.1 39

4.5. Monthly Cooling and Heating Loads The monthly cooling and heating loads (in kWh) for the whole villa are shown in Figure7a,b, respectively. It is obvious that the heating loads are much smaller than the cooling loads as expected in Riyadh and that heating is basically needed from December to February while cooling is needed over the whole year. As for the simulated effect of thermal bridges, the results in Figure7 show that the bigger the thermal bridge area ratio (Amj/Atot), the higher the load. The biggest increase caused by the bridges occurs in August, which is the worst time for this to occur for both the utility company and the consumer because this is the time of year when the peak loads and peak energy consumption occur. Sustainability 2016, 8, 560 14 of 21

(a)

(b)

FigureFigure 7. Villa’s 7. Villa’s monthly monthly loads loads for for different different thermal bridge bridge area area ratios. ratios. (a) ( Cooling;a) Cooling; (b) heating. (b) heating.

4.6. Daily Cooling and Heating Loads Sample results are presented for only two months; namely August (cooling) and January (heating). Figure 8 shows the daily cooling loads during the month of August. It is obvious that the daily loads increase with increasing thermal bridge area ratio, as expected. The corresponding results for the daily heating loads are shown for the month of January in Figure 9. Apart from using different ordinate scales on these two drawings, it is obvious that heating loads are generally much smaller than the cooling loads, which is typical under Riyadh outdoor weather conditions. Furthermore, one may observe that the effect of thermal bridges on the heating load is less pronounced than in the case of cooling in August.

Sustainability 2016, 8, 560 14 of 20

4.6. Daily Cooling and Heating Loads Sample results are presented for only two months; namely August (cooling) and January (heating). Figure8 shows the daily cooling loads during the month of August. It is obvious that the daily loads increase with increasing thermal bridge area ratio, as expected. The corresponding results for the daily heating loads are shown for the month of January in Figure9. Apart from using different ordinate scales on these two drawings, it is obvious that heating loads are generally much smaller than the cooling loads, which is typical under Riyadh outdoor weather conditions. Furthermore, one may observe that the effect of thermal bridges on the heating load is less pronounced than in the case of coolingSustainability in August. 2016, 8, 560 15 of 21 Sustainability 2016, 8, 560 15 of 21

Figure 8. Villa’s daily cooling loads in August for different thermal bridge area ratios. FigureFigure 8. 8. Villa’sVilla’s daily daily cooling cooling loads loads in inAugust August for fordifferent different thermal thermal bridge bridge areaarea ratios. ratios.

Figure 9. Daily heating loads in January for different thermal bridge area ratios. FigureFigure 9. 9. DailyDaily heating heating loads loads in inJanuary January forfor different different thermal thermal bridge bridge area area ratios. ratios. 4.7. Effect of Thermal Bridge Area Ratio on August and January Monthly Loads 4.7. Effect of Thermal Bridge Area Ratio on August and January Monthly Loads 4.7. EffectThe of results Thermal presented Bridge Area in RatioFigure on 7 August for the and mont Januaryhly cooling Monthly loads Loads are recast by plotting the The results presented in Figure 7 for the monthly cooling loads are recast by plotting the monthlyThe results load versus presented the A inmj Figure/Atot area7 for ratio the to monthly show the cooling effect loads of thermal are recast bridges by plotting in a more the explicit monthly monthly load versus the Amj/Atot area ratio to show the effect of thermal bridges in a more explicit way. loadway.versus the Amj/Atot area ratio to show the effect of thermal bridges in a more explicit way. Figure 10 shows such data for August. The results clearly indicate that the cooling load Figure 10 shows such data for August. The results clearly indicate that the cooling load increases with Amj/Atot in an almost linear fashion. The increase in the August total monthly cooling increases with Amj/Atot in an almost linear fashion. The increase in the August total monthly cooling load ranges between 4.6% for Amj/Atot = 0.02 and 14.7% for Amj/Atot = 0.08 when compared to the case load ranges between 4.6% for Amj/Atot = 0.02 and 14.7% for Amj/Atot = 0.08 when compared to the case with no thermal bridges. with no thermal bridges.

Sustainability 2016, 8, 560 15 of 20

Figure 10 shows such data for August. The results clearly indicate that the cooling load increases with Amj/Atot in an almost linear fashion. The increase in the August total monthly cooling load ranges between 4.6% for Amj/Atot = 0.02 and 14.7% for Amj/Atot = 0.08 when compared to the case withSustainability no thermal 2016, bridges.8, 560 16 of 21

Sustainability 2016, 8, 560 16 of 21

Figure 10. Effect of thermal bridges on August cooling load. Figure 10. Effect of thermal bridges on August cooling load. The corresponding results for the month of January are shown in Figure 11a for cooling and FigureThe corresponding11b for heating. It results Figuremay appear 10. for Effect the counter of month thermal intuitive of bridges January that on Augustcooling are shown cooling is needed inload. Figure in January, 11a forbut coolingthere and Figureare days 11b where for heating. the outdoor It may temperat appearure counter is moderately intuitive cold, that thereby cooling reducing is needed the heat in loss January, from the but there The corresponding results for the month of January are shown in Figure 11a for cooling and arevilla days envelope where theto a outdoorlevel just temperaturebelow internal is heat moderately gains, therefore cold, therebyrequiring reducing some cooling. the heat The lossresults from the Figure 11b for heating. It may appear counter intuitive that cooling is needed in January, but there villainenvelope Figure 11a to indicate a level justclearly below thatinternal the monthly heat gains,cooling therefore load in January requiring drops some monotonically cooling. The and results in almostare days linearly where with the A outdoormj/Atot as temperat larger thermalure is moderately bridges enhance cold, thereby heat loss re ducingthrough the the heat walls, loss thereby from the Figure 11a indicate clearly that the monthly cooling load in January drops monotonically and almost reducingvilla envelope the cooling to a levelload. justThe below reduction internal in the heat cooling gains, load therefore ranges requiring from 7.9% some for cooling. Amj/Atot The= 0.02 results to linearly with Amj/Atot as larger thermal bridges enhance heat loss through the walls, thereby reducing 22.9%in Figure for A 11amj/A indicatetot = 0.08. clearly These that results the monthlyindicate coolingthat higher load thermalin January bridge drops area monotonically ratios have anda thebeneficial coolingalmost load.linearlyeffect Thein with January, reduction Amj/A astot they as in larger thereduce cooling thermal coolin load gbridges loads, ranges whichenhance from is thehe 7.9%at opposite loss for through A mjof /Athe totthetrend= walls, 0.02 observed tothereby 22.9% for Amjin/A reducingAugust.tot = 0.08. Asthe for These cooling the resultsheating load. The indicateload, reduction the thatresults higherin inthe Figure cooling thermal 10b load bridgeshow ranges that area fromit increases ratios 7.9% have for with A amj beneﬁcialthe/Atot thermal = 0.02 effect to in January,bridge22.9% as area theyfor ratio, A reducemj/A astot expected,= cooling0.08. These because loads, results whichlarger indicate thermal is the oppositethat bridges higher increase of thethermal trend heat bridge loss observed from area the inratios villa August. haveand, Asa for thetherefore, heatingbeneficial load, increase effect the inthe results January, heating in as Figureload they on reduce 10 theb showHVAC coolin that equipment.g loads, it increases which However, is with the opposite thethe behavior thermal of the bridgeis trend not quite observed area as ratio, as expected,linearin August. as because we have As for larger seen the in thermalheating the cooling load, bridges loads. the results increase in Figure heat loss 10bfrom show the that villa it increases and, therefore, with the thermal increase the bridge area ratio, as expected, because larger thermal bridges increase heat loss from the villa and, heating load on the HVAC equipment. However, the behavior is not quite as linear as we have seen in therefore, increase the heating load on the HVAC equipment. However, the behavior is not quite as the coolinglinear as loads. we have seen in the cooling loads.

(a) (b)

Figure 11. Effect of thermal bridges on January cooling and heating loads. (a) Cooling; (b) heating.

(a) (b) 4.8. Effect of Thermal Bridge Area Ratio on Yearly Cooling and Heating Loads Figure 11. Effect of thermal bridges on January cooling and heating loads. (a) Cooling; (b) heating. FigureThe effect 11. Effect of A ofmj/A thermaltot on the bridges yearly on cooling January load cooling of the and villa heating is shown loads. in (a Figure) Cooling; 12a. ( bThe) heating. load increases4.8. Effect almost of Thermal linearly Bridge with Area Amj/A Ratottio. The on Yearly yearly Cooling load ranges and Heating from 69,161 Loads kWh/year at Amj/Atot = 0 to 76,624 kWh/year at Amj/Atot = 0.08. The increase in the yearly load compared to the case with no mj tot thermalThe bridges effect ranges of A /Afrom on2.9% the for yearly Amj/A coolingtot = 0.02 load to 10.8% of the for villa Amj is/A showntot = 0.08. in TheFigure corresponding 12a. The load increases almost linearly with Amj/Atot. The yearly load ranges from 69,161 kWh/year at Amj/Atot = 0 to

76,624 kWh/year at Amj/Atot = 0.08. The increase in the yearly load compared to the case with no thermal bridges ranges from 2.9% for Amj/Atot = 0.02 to 10.8% for Amj/Atot = 0.08. The corresponding

Sustainability 2016, 8, 560 16 of 20

4.8. Effect of Thermal Bridge Area Ratio on Yearly Cooling and Heating Loads

The effect of Amj/Atot on the yearly cooling load of the villa is shown in Figure 12a. The load increases almost linearly with Amj/Atot. The yearly load ranges from 69,161 kWh/year at Amj/Atot = 0 to 76,624 kWh/year at Amj/Atot = 0.08. The increase in the yearly load compared to the case with no thermal bridges ranges from 2.9% for Amj/Atot = 0.02 to 10.8% for Amj/Atot = 0.08. The corresponding Sustainability 2016, 8, 560 17 of 21 results for the yearly heating load are shown in Figure 12b. Although the load increases monotonically with Amjresults/Atot ,for the the behavior yearly isheating not as load linear are asshown in the in cooling Figure load.12b. TheAlthough yearly the heating load increases load increases from 443monotonically kWh/year with without Amj/Atot thermal, the behavior bridges is not to as 482 linear kWh/year as in the cooling with thermal load. The bridges yearly heating of area ratio load increases from 443 kWh/year without thermal bridges to 482 kWh/year with thermal bridges of Amj/Atot = 0.08, representing an increase of about 9%. The nonlinear behavior of the heating load may be attributedarea ratio to A themj/A facttot = that0.08, representing internal heat an gainsincrease tend of about to reduce 9%. The the nonlinear heating behavior load and of the that heating these loads load may be attributed to the fact that internal heat gains tend to reduce the heating load and that are not uniform as they change according to speciﬁc schedules. these loads are not uniform as they change according to specific schedules.

78000 500

76000 480 ) ) r r 74000 /yea h W Wh/yea 460 k k ( ( 72000 y,c y,h Q Q 440 70000

68000 420 02468 02468 Amj/Atot (%) Amj/Atot (%) (a) (b)

Figure 12. Effect of thermal bridges on yearly loads. (a) Cooling; (b) heating. Figure 12. Effect of thermal bridges on yearly loads. (a) Cooling; (b) heating. 4.9. Energy Savings and Environmental Advantages of Eliminating Thermal Bridges 4.9. Energy SavingsThe effects and of Environmentalthermal bridges Advantagesresulting from of Eliminatingmortar joints Thermalcan be eliminated Bridges by using tongue Theand effects groove of insulated thermal building bridges blocks. resulting In this from configuration, mortar joints the thermal can be insulation eliminated layer byprotrudes using tongue from one side of the block (tongue) with a corresponding recess on the other side of the block and groove insulated building blocks. In this conﬁguration, the thermal insulation layer protrudes (groove). When these blocks are stacked above each other in a wall, the tongue engages into the from onegroove side ofthereby the block ensuring (tongue) the continuity with a of corresponding the insulation layer. recess For on a typical the other 1.2-cm side mortar of the joint block with (groove). When thesea typical blocks 20-cm are height stacked of insulated above each block other (TB inrati ao wall,of 0.06), the the tongue results engages of the yearly into thecooling groove and thereby ensuringheating the continuity loads and the of theassociated insulation yearly layer. electric For loads a typical (for HVAC 1.2-cm equipment mortar jointonly) withare in a Table typical 4 20-cm height ofbelow. insulated block (TB ratio of 0.06), the results of the yearly cooling and heating loads and the associated yearly electric loads (for HVAC equipment only) are in Table4 below. Table 4. Yearly cooling, heating and associated electric equipment loads for a TB ratio of 0.06 compared to the case with no thermal bridges. Table 4. Yearly cooling, heating and associated electric equipment loads for a TB ratio of 0.06 compared Cooling Heating Fan Electric Total Electric to theTB case with no thermalCooling bridges. Heating Electric Electric R-Value Energy Energy Area Load Load Energy Energy (m2·K/W) Consumption Consumption Ratio (kWh/year) (kWh/year) ConsumptionCooling ConsumptionHeating Electric (kWh/year)Fan Electric(kWh/year)Total Electric TB Area R-Value Cooling Load Heating Load(kWh/year)Electric (kWh/year) Energy Energy Energy Energy Ratio (m2¨ K/W) (kWh/year) (kWh/year) Consumption Consumption 0.0 2.66 68,913 443 16,794Consumption 96Consumption 11,942 28,832 (kWh/year) (kWh/year) 0.06 1.52 74,936 470 18,219(kWh/year) 114(kWh/year) 13,123 31,456 0.0 2.66 68,913 443 16,794 96 11,942 28,832 0.06Based 1.52on Table 4 above, 74,936 the electric 470 energy savings 18,219 brought about 114 by eliminating 13,123 mortar joint 31,456 thermal bridges is 2624 kWh per year for this villa alone. The estimated number of residential units in Riyadh is about 960,000 [25]. Villas represent about 60% of residential units, while apartments Based on Table4 above, the electric energy savings brought about by eliminating mortar joint represent about 40%. The floor area of the average apartment is about 40% of that of the villa. thermalTherefore, bridges isthe 2624 saving kWh weighing per year factor for of this a re villasidential alone. unit The is 0.6 estimated × 1 + 0.4 × number0.4 = 0.76, of i.e residential., the saving units in Riyadhper is about residential 960,000 unit [ 25on]. average Villas representis 0.76 × the about savings 60% per of villa. residential This would units, translate while to apartments yearly energy represent about 40%.savings The of ﬂoor1914 million area of kWh the of average electricity apartment in the city of is Riyadh about alone. 40% of that of the villa. Therefore, the

Sustainability 2016, 8, 560 17 of 20 saving weighing factor of a residential unit is 0.6 ˆ 1 + 0.4 ˆ 0.4 = 0.76, i.e., the saving per residential unit on average is 0.76 ˆ the savings per villa. This would translate to yearly energy savings of 1914 million kWh of electricity in the city of Riyadh alone. According to the U.S. Energy Information Administration [26], 1 kWh of generated electricity produces 1.22 pounds of CO2 emissions from plants energized by natural gas and 1.64 pounds for plants energized by distillate oil. Assuming roughly equal use of both fuels in Saudi Arabia, the average emissions per kWh generated is estimated to be 1.43 pounds. Further assuming about 10% losses in the transmission and distribution network, the amount of CO2 that could be saved by eliminating 6 mortar joint thermal bridges is estimated at 1.38 ˆ 10 tons CO2 per year, and this is for the city of Riyadh alone.

5. Summary and Concluding Remarks The effects of thermal bridges in insulated building walls on the yearly, monthly and daily cooling and heating loads in a typical villa in Riyadh were investigated by using a commercial whole building energy simulation computer package (HAP). The thermal bridges considered in this study are solely due to mortar joints between insulated building blocks. The villa has two levels with a total floor area of 400 m2 with all walls exposed to the ambient environment (detached home). All HVAC loads found in such a typical villa were considered with schedules based on local lifestyles. The thermal bridge effect was simulated in the whole building energy analysis by reducing the wall thermal resistance by a percentage that corresponds to the bridge to wall area ratio and the nominal thickness of the insulation layer. These percentage reductions were obtained from a graphical correlation developed based on the detailed and rigorous 2D dynamic analysis of mortar joint effects on heat transmission through wall sections. The results indicate that the yearly cooling load of the villa increases almost linearly with the TB area ratio (Amj/Atot). The increase varies from about 3% for Amj/Atot = 0.02 to about 11% for Amj/Atot = 0.08. On a monthly basis, the variation of the cooling load with Amj/Atot is also approximately linear; however, the rate of increase is higher during summer months. In August, for example, the monthly cooling load increases by about 5% for Amj/Atot = 0.02 up to about 15% for Amj/Atot = 0.08. In winter, results show that heating is required mainly in December, January and February, starting from late night to late morning, while cooling is required from roughly noon time to late in the evening on some days. The heating loads are generally very small compared to the cooling loads in spite of cold outdoor weather in January, for example, because of internal heat generation from various sources within the villa. The results show further that the monthly heating load for that month increases with the thermal bridge area ratio; however, the variation is not as linear as observed earlier. The same behavior is observed for the yearly heating loads. It should be noted, however, that people seldom use mechanical cooling in winter in Riyadh; instead, they employ natural ventilation by allowing cold outdoor air into inhibited spaces to absorb heat generated indoors, but this was not considered in this study. Because yearly heating loads are generally insignificant compared to cooling loads, the percentage effects of thermal bridges on heating reported earlier in the text may cause unwarranted concern. One should keep in mind that the absolute values of those effects (on heating) are almost negligible and therefore may be ignored under similar ambient conditions. The total yearly load (cooling plus heating) was found to increase by about 3% for Amj/Atot = 0.02 to about 11% for Amj/Atot = 0.08, which are the same percentages obtained for the cooling load, as expected. It should also be noted that the percentage increases in loads as a result of thermal bridges obtained from whole building energy analysis are much smaller than the corresponding values obtained from the 2D dynamic study of the transmission load across the wall section, because all other loads are considered in the former analysis, and these loads are almost unaffected by thermal bridges. The results of this study highlight the importance of the effects of thermal bridges resulting from mortar joints between building blocks. These effects should not be ignored at the design stage, as Sustainability 2016, 8, 560 18 of 20 they tend to increase design loads and therefore equipment size, and at the operational stage, as they increase the annual energy consumption. Most of the literature on thermal bridges focuses on bridges due to structural elements, while very little attention has been given to mortar joints. It is hoped that this study will fill this gap.

Acknowledgments: This project was funded by the National Plan for Science, Technology and Innovation (MAARIFAH), King Abdulaziz City for Science and Technology, Kingdom of Saudi Arabia, Award Number: 08-ENE376-2.Sustainability 2016, 8, 560 19 of 21 Author Contributions:Acknowledgments:The This paper project is awas part funded ofa by large the National research Plan project for Science, in the Technology area of and energy Innovation conservation in buildings. All(MAARIFAH), four authors King participatedAbdulaziz City inforthe Science planning and Technology, of this project. Kingdom The of Saudi main Arabia, idea Award of this Number: particular part of the study was08-ENE376-2. conceived primarily by Sami Al-Sanea through discussions with Mohamed F. Zedan. The paper was writtenAuthor primarily Contributions: by Mohamed The paper F. Zedan is a part with of a contributions large research proj fromect Samiin the Al-Saneaarea of energy and conservation Abdulaziz in Al-Mujahid. Zeyad Al-Suhaibanibuildings. Allwent four throughauthors participated the manuscript in the planning and made of this valuable project. The suggestions, main idea of therebythis particular improving part of the paper. The whole buildingthe study was energy conceived analysis primarily was by conducted Sami Al-Sanea by th Mohamedrough discussions F. Zedan with Mohamed and verified F. Zedan. by Zeyad The paper Al-Suhaibani . The 2D studywas waswritten conducted primarily by mainly Mohamed by SamiF. Zedan Al-Sanea with contributions with some from help Sami from Al-Sanea Abdulaziz and Abdulaziz Al-Mujahid and Mohamed F.Al-Mujahid. Zedan. Zeyad Al-Suhaibani went through the manuscript and made valuable suggestions, thereby improving the paper. The whole building energy analysis was conducted by Mohamed F. Zedan and verified Conflicts of Interest: The authors declare no conflict of interest. The funding sponsors had no role in the design by Zeyad Al-Suhaibani. The 2D study was conducted mainly by Sami Al-Sanea with some help from of the study;Abdulaziz in the collection, Al-Mujahid and analyses Mohamed or interpretationF. Zedan. of data; in the writing of the manuscript. However, they encouraged the publication of the results. Conflicts of Interest: The authors declare no conflict of interest. The funding sponsors had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript. However, they Abbreviationsencouraged the publication of the results. The following abbreviations are used in this manuscript: Abbreviations 2D: Two-dimensional 3D: The following abbreviationsThree-dimensional are used in this manuscript: ASHRAE: 2D: Two-dimensionalAmerican Society of Heating, Refrigeration and Air Conditioning Engineers CDD: 3D: Three-dimensionalCooling degree days HDD: ASHRAE: AmericanHeating Society degreeof Heating, days Refrigeration and Air Conditioning Engineers HAP: CDD: Cooling degreeHourly days Analysis Program mj: HDD: Heating degreeMortar days joint MAARIFAH:HAP: Hourly AnalysisLocal Program name in Saudi Arabia for the National Plan for Science, Technology and Innovation R-value: mj: Mortar joint Wall thermal resistance MAARIFAH: Local name in Saudi Arabia for the National Plan for Science, Technology and Innovation STD: Standard R-value: Wall thermal resistance TB: Thermal bridge STD: Standard TR: TB: Thermal bridgeTon Refrigeration TR: Ton Refrigeration Appendix A Appendix A

Figure 1. Picture of an insulated building block. Sustainability 2016, 8, 560 19 of 20

Appendix B

Table 1. Nomenclature.

Symbol Meaning A heat transfer area (m2) c specific heat (J/kg.K) Hb building block height (m) Hmj mortar joint height (m) h heat-transfer coefficient (W/m2.K) 2 Is solar radiation flux (W/m ) k thermal conductivity (W/m¨ K) L wall thickness (m) Lins insulation thickness (m) N number of layers in wall Q daily or yearly transmission load (kWh/m2¨ day or kWh/m2¨ year) q heat flux or instantaneous transmission load (W/m2) 2 Rd-value wall dynamic thermal resistance (m ¨ K/W) 2 Rn-value wall nominal (static) thermal resistance (m ¨ K/W) T temperature (˝C or K) t time (s) x, y coordinate directions (m) Greek Letters λ solar absorptivity ρ density (kg/m3) Subscripts c convection f fluid (ambient air) i inside j layer number in wall mj mortar joint N inside layer in wall o outside r radiation 0 initial (t = 0) 1 outside layer in wall

References

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